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Hybrid fluid models, consisting of two sectors with more weakly and more strongly self-interacting degrees of freedom coupled consistently as in the semi-holographic framework, have been shown to exhibit an attractor surface for Bjorken flow. Retaining only the simple viscid fluid descriptions of both sectors, we find that, on the attractor surface, the hydrodynamization times of both subsectors decrease with increasing total energy density at the respective point of hydrodynamization following a conformal scaling, reach their minimum values, and subsequently rise rapidly. The minimum values are obtained when the respective energy densities are of the order of the inverse of the dimensionful inter-system coupling. Restricting to attractor curves which can be matched to glasma models at a time set by the saturation scale for both $p$-$p$ and Pb-Pb collisions, we find that the more weakly coupled sector hydrodynamizes much later, and the strongly coupled sector hydrodynamizes earlier in $p$-$p$ collisions, since the total energy densities at the respective hydrodynamization times of these sectors fall inside and outside of the conformal window. This holds true also for phenomenologically relevant solutions that are significantly away from the attractor surface at the time we match to glasma models.